Thermodynamic symmetry resolved entanglement entropies in integrable systems

TL;DR

This paper introduces a novel method combining thermodynamic Bethe ansatz and large deviation theory to compute symmetry-resolved entanglement entropies in integrable systems, with explicit formulas and validation against numerical simulations.

Contribution

It develops a general approach to calculate symmetry-resolved entanglement entropies in integrable models, providing explicit formulas and applications to quantum quenches.

Findings

Derived explicit formula for von Neumann symmetry-resolved entanglement entropy.

Validated the approach with numerical simulations on the XXZ spin chain.

Provided analytic predictions for entanglement entropy after quantum quenches.

Abstract

We develop a general approach to compute the symmetry-resolved R\'enyi and von Neumann entanglement entropies (SREE) of thermodynamic macrostates in interacting integrable systems. Our method is based on a combination of the thermodynamic Bethe ansatz and the G\"artner-Ellis theorem from large deviation theory. We derive an explicit simple formula for the von Neumann SREE, which we show to coincide with the thermodynamic Yang-Yang entropy of an effective macrostate determined by the charge sector. Focusing on the XXZ Heisenberg spin chain, we test our result against iTEBD calculations for thermal states, finding good agreement. As an application, we provide analytic predictions for the asymptotic value of the SREE following a quantum quench.